This reduced model emphasizes
three groups of variables:
slaved variables \(z_1,\ldots ,z_{l-1}\) , which are faster than \(\delta ^{b_l}\) ,
driving variables \(z_l\) , which have timescale \(\delta ^{b_l}\) ,
and quenched variables \(z_{l+1},\, \ldots , \, z_m\) , which are slower than \(\delta ^{b_l}\) .
If regularity and hyperbolicity conditions are satisfied (see [1]} and Section REF ), then the solutions
of system (REF ) converge to the solutions
of system (REF ) when \(\epsilon _k \rightarrow 0\) 
for \( 1 \le k \le l-1\)  (see the Corollary of Theorem A in
[1]}).
